Prove the inequality a ^ 5 + B ^ 5 ≥ a ^ 3B ^ 2 + A ^ 2B ^ 3 (a > 0, b > 0)

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• 1. A proof of mathematical inequality P ≥ 0, Q ≥ 0, P + q = 1 AP + BQ and √ (A & # 178; P + B & # 178; q) ratio
• 2. Algebraic inequality 1 Let x, y, Z ∈ R +, prove: X √ [x / (1 + YZ)] + y √ [y / (1 + ZX)] + Z √ [Z / (1 + XY)] ≥ 3 / √ (1 + XYZ)
• 3. A proof of inequality Given that a, B and C are positive real numbers and ab + BC + Ca = 3, it is proved that a ^ 2 + B ^ 2 + C ^ 3 + 3ABC ≥ 6 That's right!
• 4. Prove 1-p (a ~) - P (b ~)
• 5. FX = x (1-x & # 178;) for fixed value (mean inequality)
• 6. The range of y = x + x-3 / 1 (x is greater than 3) is determined by means inequality method
• 7. Given that X and y are greater than zero. 1 / x + 2 / y + 1 = 2, then the minimum value of 2x + y is the mean inequality,
• 8. Mean inequality when 0
• 9. Using the mean inequality method to find the range and the maximum value: y = x ^ 2 × (3-2x)
• 10. Find the maximum value of F (x), using the mean inequality! Let x > - 1, find the inequality of the maximum mean value of F (x) = (x + 5) * (x + 2) / (x + 1)~ And the maximum~~~~
• 11. Let a and B be positive numbers, and prove the following inequality (1.) B / A + A / b ≥ 2 (2.) a + 1 / a ≥ 2
• 12. b> A > 0 proves B-A / b
• 13. Given a set, a = {x | X & # 178; - # 8722; 1} = 0, then the following formula is correct () ①1∈A ②{-1}∈A ③φ ⊆A④{ 1,−1}⊆A A. 1 B.2 C.3 D.4 That box is about subsets of symbols, I do not know how to make summer self-study Especially the third one is not to be added{
• 14. (1) 3 () 2; (2) - 2 () 0; (3) a & # 178; () 0; (4) - A & # 178; () 0 [use unequal sign to connect the following numbers or formulas] （1）3（）2；（2）-2（）0；（3）a²（）0；（4）-a²（）0 What language in life can be replaced by these unequal symbols (1) <: less than___________________ (2) Greater than___________________ (3) ≥: greater than or equal to________________ (4) ≤: less than or equal to________________
• 15. It is known that a is the smallest positive integer, B and C are rational numbers, and have | 2 + a | + (a + C) & # 178; = 0. Find the value of 4AB + C / - a # 178; + C & # 178; + 4
• 16. The following formula is correct: a. √ A & # 178; = a B. √ a ·√ B = √ AB C. √ AB = √ a '√ B D. √ A / b = √ A / √ B
• 17. If a-178; - A
• 18. It is proved that [2 [under radical (n + 1) - 1]] < 1 + 1 / radical 2 + 1 / radical 3 + +Thank you very much RT
• 19. Prove by definition: if a > b > 0, C
• 20. It is known that a > b > 0, C > d > 0, a of B = C of D. it means that ① (a + b) / a = (c + D) / C. ② (a-b) / b = (C-D) / d Please use the eighth grade knowledge of Shandong education press to answer, thank you